The aggressive era of stop-and-frisk policing in New York City is, in every sense of the word, on trial: the subject of a high-stakes federal court case, scorching denunciations from civil rights leaders and emotional calls for its dismantlement by liberal lawmakers.

But in a stand that is surprising black leaders and worrying some allies, William C. Thompson Jr., the sole African-American candidate for mayor, is steadfastly unwilling to join the tear-it-down chorus.

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Mr. Thompson is now bucking the left wing of his party on three fronts: by pledging to keep stop-and-frisk operations as a crime-fighting tool; proposing an inspector general who operates within the Police Department, rather than outside of it (“I don’t want to create additional bureaucracy,” he said); and opposing a City Council bill that would open state courts to legal claims of racial profiling by the Police Department. (He said it would divert precious city finances to endless legal bills.)